What is the method to determine the weighted median, instead of the weighted mean, for single-arm meta-analysis?

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To determine the weighted median for single-arm meta-analysis, the following steps can be taken:

1. Collect the individual study weights and estimates of the outcome of interest (e.g., response rate or survival rate) from each included study.

2. Sort the individual study estimates in ascending order.

3. Calculate the cumulative sum of the study weights.

4. Determine the midpoint of the total weight (i.e., 0.5 times the sum of all weights).

5. Identify the study with the estimate that corresponds to the midpoint of the total weight. This is the weighted median estimate.

If there are an even number of studies, the median is the average of the two middle values.